# Analysis of thermo-elastic problems using the improved element-free Galerkin method

## Abstract

The improved element-free Galerkin method (IEFG) is presented to deal with thermo-elastic problems. This mesh-free method is a combination between the element-free Galerkin method and the improved moving least-square approximation. It has not the Kronecker delta property, and the penalty method is used to impose the essential boundary conditions. In this paper, linear and stationary thermo-elasticity is treated. To solve the thermo-elastic problem, this latter is decoupled into two separate parts: first, the heat transfer problem is analyzed to reach the temperature field, which is used as input in the mechanical problem to calculate the displacement field and then the stress fields. Numerical examples with different boundary conditions are illustrated. The performance and the accuracy of the IEFG method are approved when obtained results are compared to finite-element results and analytical solution.

- Authors:

- National School of Engineering, University of Monastir, Laboratory of Mechanical Engineering (Tunisia)

- Publication Date:

- OSTI Identifier:
- 22769346

- Resource Type:
- Journal Article

- Journal Name:
- Computational and Applied Mathematics

- Additional Journal Information:
- Journal Volume: 37; Journal Issue: 2; Other Information: Copyright (c) 2018 SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0101-8205

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 97 MATHEMATICAL METHODS AND COMPUTING; ANALYTICAL SOLUTION; BOUNDARY CONDITIONS; COMPARATIVE EVALUATIONS; FINITE ELEMENT METHOD; HEAT TRANSFER; LEAST SQUARE FIT

### Citation Formats

```
Debbabi, Imen, and BelhadjSalah, Hédi.
```*Analysis of thermo-elastic problems using the improved element-free Galerkin method*. United States: N. p., 2018.
Web. doi:10.1007/S40314-016-0401-1.

```
Debbabi, Imen, & BelhadjSalah, Hédi.
```*Analysis of thermo-elastic problems using the improved element-free Galerkin method*. United States. doi:10.1007/S40314-016-0401-1.

```
Debbabi, Imen, and BelhadjSalah, Hédi. Tue .
"Analysis of thermo-elastic problems using the improved element-free Galerkin method". United States. doi:10.1007/S40314-016-0401-1.
```

```
@article{osti_22769346,
```

title = {Analysis of thermo-elastic problems using the improved element-free Galerkin method},

author = {Debbabi, Imen and BelhadjSalah, Hédi},

abstractNote = {The improved element-free Galerkin method (IEFG) is presented to deal with thermo-elastic problems. This mesh-free method is a combination between the element-free Galerkin method and the improved moving least-square approximation. It has not the Kronecker delta property, and the penalty method is used to impose the essential boundary conditions. In this paper, linear and stationary thermo-elasticity is treated. To solve the thermo-elastic problem, this latter is decoupled into two separate parts: first, the heat transfer problem is analyzed to reach the temperature field, which is used as input in the mechanical problem to calculate the displacement field and then the stress fields. Numerical examples with different boundary conditions are illustrated. The performance and the accuracy of the IEFG method are approved when obtained results are compared to finite-element results and analytical solution.},

doi = {10.1007/S40314-016-0401-1},

journal = {Computational and Applied Mathematics},

issn = {0101-8205},

number = 2,

volume = 37,

place = {United States},

year = {2018},

month = {5}

}